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The aim is to investigate the behaviour of (homomorphic images of) periodic linear groups which are factorized by mutually permutable subgroups. Mutually permutable subgroups have been extensively investigated in the finite case by several authors, among which, for our purposes, we only cite J. C. Beidleman and H. Heineken (2005). In a previous paper of ours (see M. Ferrara, M. Trombetti (2022)) we have been able to generalize the first main result of J. C. Beidleman, H. Heineken (2005) to periodic...

Periodic-by-nilpotent linear groups

B. A. F. Wehrfritz (2010)

Rendiconti del Seminario Matematico della Università di Padova

Permutability of centre-by-finite groups

Brunetto Piochi (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let $G$ be a group and $m$ be an integer greater than or equal to $2$ . $G$ is said to be $m$ -permutable if every product of $m$ elements can be reordered at least in one way. We prove that, if $G$ has a centre of finite index $z$ , then $G$ is $(1+[z/2])$ -permutable. More bounds are given on the least $m$ such that $G$ is $m$ -permutable.

Permutations with Kazhdan-Lusztig polynomial $P_{i d, w} (q) = 1 + q^{h}$ . With an appendix by Sara Billey and Jonathan Weed.

Billey, Alexander Woo (2009)

The Electronic Journal of Combinatorics [electronic only]

Plane Motion Groups and Virtual Poincaré Duality of Dimension Two.

H. Müller, B. Eckman (1982)

Inventiones mathematicae

Platonic triangles of groups.

Alperin, Roger C. (1998)

Experimental Mathematics

P-localization of some classes of groups.

Augusto Reynol Filho (1993)

Publicacions Matemàtiques

The aim for the present paper is to study the theory of P-localization of a group in a category C such that it contains the category of the nilpotent groups as a full sub-category. In the second section we present a number of results on P-localization of a group G, which is the semi-direct product of an abelian group A with a group X, in the category G of all groups. It turns out that the P-localized (GP) is completely described by the P-localized XP of X, A and the action w of X on A. In the third...

Plongements quasiisométriques du groupe de Heisenberg dans $L^{p}$ , d’après Cheeger, Kleiner, Lee, Naor

Pierre Pansu (2006/2007)

Séminaire de théorie spectrale et géométrie

Bref survol du théorème de non-plongement de J. Cheeger et B. Kleiner pour le groupe d’Heisenberg dans $L^{1}$ .

P-nilpotent completion is not idempotent.

Geok Choo Tan (1997)

Publicacions Matemàtiques

Let P be an arbitrary set of primes. The P-nilpotent completion of a group G is defined by the group homomorphism η: G → GP' where GP' = inv lim(G/ΓiG)P. Here Γ2G is the commutator subgroup [G,G] and ΓiG the subgroup [G, Γi−1G] when i > 2. In this paper, we prove that P-nilpotent completion of an infinitely generated free group F does not induce an isomorphism on the first homology group with ZP coefficients. Hence, P-nilpotent completion is not idempotent. Another important consequence of...

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$p$ -adic completions and automorphisms of nilpotent groups

Parabolic isometries of CAT(0) spaces and CAT(0) dimensions.

Parametrized braid groups of Chevalley groups.

Partial Homogeneity in Locally Finite Groups.

PBW-bases of quantum groups.

P-equivalence de groupes nilpotents.

Periodic groups saturated by the group $U_{3} (9)$ .

Periodic groups saturated with the groups $L_{2} (p^{n})$ .

Periodic linear groups factorized by mutually permutable subgroups